What is the derivative of (-2x/((1+x^2)^2)) ?

The derivative of (-2x/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)

What is the first derivative of (-2x/((1+x^2)^2)) ?

The first derivative of (-2x/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)

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\frac{d}{d x} (\frac{- 2 x}{( 1 + x ^{2} ) ^{2}})

- \frac{2 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{- 2 x}{( 1 + x ^{2} ) ^{2}})

Simplify

\frac{- 2 x}{( 1 + x ^{2} ) ^{2}} : - \frac{2 x}{( 1 + x ^{2} ) ^{2}}

= \frac{d}{d x} (- \frac{2 x}{( 1 + x ^{2} ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{d}{d x} (\frac{x}{( 1 + x ^{2} ) ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 2 \cdot \frac{\frac{d x}{d x} ( 1 + x ^{2} ) ^{2} - \frac{d}{d x} ( ( 1 + x ^{2} ) ^{2} ) x}{( ( 1 + x ^{2} ) ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((1 + x^{2})^{2}) = 4 x (1 + x^{2})

= - 2 \cdot \frac{1 \cdot ( 1 + x ^{2} ) ^{2} - 4 x ( 1 + x ^{2} ) x}{( ( 1 + x ^{2} ) ^{2} ) ^{2}}

Simplify

- 2 \cdot \frac{1 \cdot ( 1 + x ^{2} ) ^{2} - 4 x ( 1 + x ^{2} ) x}{( ( 1 + x ^{2} ) ^{2} ) ^{2}} : - \frac{2 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{3}}

= - \frac{2 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{3}}

y = e^{7}

y^{^{''}} - 6 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 7

e^{y} (1 + x^{2}) d y - 2 x (1 + e^{y}) d x = 0

\int 2 e x + 8 x^{3} + 6 x d x

\int_{0}^{1} \frac{61}{4 x - 1} d x

What is the derivative of (-2x/((1+x^2)^2)) ?
The derivative of (-2x/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)
What is the first derivative of (-2x/((1+x^2)^2)) ?
The first derivative of (-2x/((1+x^2)^2)) is -(2(-3x^2+1))/((1+x^2)^3)